[Lois de conservation hyperboliques sur les variétés à faible régularité]
Nous proposons une formulation du problème de Cauchy avec conditions aux limites pour les lois de conservation hyperboliques nonlinéaires posées sur une variété différentiable munie d'une forme volume, avec ou sans bord ; notre étude couvre, en particulier, le cas important des variété Lorentzienne. Nous supposons une régularité limitée sur la géometrie de la variété. Pour ce problème nous démontrons l'existence et l'unicité d'un semi-groupe de solutions faibles satisfaisant à des conditions d'entropie et à des conditions aux limites convenablement définies.
We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the important case of Lorentzian manifolds. Only limited regularity is assumed on the geometry of the manifold. For this problem, we establish the existence and uniqueness of an semi-group of weak solutions satisfying suitable entropy and boundary conditions.
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@article{CRMATH_2008__346_9-10_539_0,
author = {LeFloch, Philippe G. and Okutmustur, Baver},
title = {Hyperbolic conservation laws on manifolds with limited regularity},
journal = {Comptes Rendus. Math\'ematique},
pages = {539--543},
publisher = {Elsevier},
volume = {346},
number = {9-10},
year = {2008},
doi = {10.1016/j.crma.2008.03.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.03.017/}
}
TY - JOUR AU - LeFloch, Philippe G. AU - Okutmustur, Baver TI - Hyperbolic conservation laws on manifolds with limited regularity JO - Comptes Rendus. Mathématique PY - 2008 SP - 539 EP - 543 VL - 346 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.03.017/ DO - 10.1016/j.crma.2008.03.017 LA - en ID - CRMATH_2008__346_9-10_539_0 ER -
%0 Journal Article %A LeFloch, Philippe G. %A Okutmustur, Baver %T Hyperbolic conservation laws on manifolds with limited regularity %J Comptes Rendus. Mathématique %D 2008 %P 539-543 %V 346 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.03.017/ %R 10.1016/j.crma.2008.03.017 %G en %F CRMATH_2008__346_9-10_539_0
LeFloch, Philippe G.; Okutmustur, Baver. Hyperbolic conservation laws on manifolds with limited regularity. Comptes Rendus. Mathématique, Tome 346 (2008) no. 9-10, pp. 539-543. doi : 10.1016/j.crma.2008.03.017. http://www.numdam.org/articles/10.1016/j.crma.2008.03.017/
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